Iterative Twofold Line Integral Convolution for Texture-Based Vector Field Visualization

Iterative twofold convolution is proposed as an efficient high-quality two-stage filtering method for dense texture-based vector field visualization. The first stage employs a compact filter, evaluated via Lagrangian particle tracing. This stage facilitates a flexible design of filters and is a means of avoiding numerical diffusion. The second stage uses semi-Lagrangian texture advection with iterative alpha blending to efficiently implement a large-scale exponential filter. A discussion of frequency-space properties and adequate sampling rates shows that this order of convolution operations permits large integration step sizes without loss of quality. Twofold convolution can be used for steady and unsteady vector fields, dye and noise advection, as well as vector fields on flat manifolds or curved surfaces. The proposed approach is prepared for an efficient GPU implementation to achieve interactive visualizations.